In [369]:
%matplotlib inline

import matplotlib
import numpy as np
import matplotlib.pyplot as plt

import numpy as np
import time
In [370]:
def countingSort(arr, exp1, b=2): 
  
    n = len(arr) 
  
    # The output array elements that will have sorted arr 
    output = [0] * (n) 
  
    # initialize count array as 0 
    count = [0] * (b) 
  
    # Store count of occurrences in count[] 
    for i in range(0, n): 
        index = (arr[i]/exp1) 
        

        count[ int((index)%b) ] += 1
  
    # Change count[i] so that count[i] now contains actual 
    #  position of this digit in output array 
    for i in range(1,b): 
        count[i] += count[i-1] 
  
    # Build the output array 
    i = n-1
    while i>=0: 
        index = (arr[i]/exp1) 
        output[ count[ int((index)%b) ] - 1] = arr[i] 
        
        count[ int((index)%b) ] -= 1
        i -= 1
  
    # Copying the output array to arr[], 
    # so that arr now contains sorted numbers 
    i = 0
    for i in range(0,len(arr)): 
        arr[i] = output[i] 
In [371]:
# Method to do Radix Sort 
def radixSort(arr, b=2): 
  
    # Find the maximum number to know number of digits 
    max1 = max(arr) 
  
    # Do counting sort for every digit. Note that instead 
    # of passing digit number, exp is passed. exp is 10^i 
    # where i is current digit number 
    exp = 1
    while max1/exp > 0: 
        countingSort(arr,exp, b) 
        exp *= b
In [282]:
def timeIt(N, exp=False, var_b=False):
    timeList = list()
    for n in N:
        if exp:
            arr = [np.random.randint(0, 2**n) for _ in range(n)]
            arr.append(2**n)
        else:
            arr = [np.random.randint(0, n) for _ in range(n)]
            arr.append(n)
        
        start = time.time()
        if 
        radixsort(arr) 
        end = time.time()
    
        dt = end - start
        timeList.append(dt)
        
    return timeList
In [365]:
 
In [ ]:
 

If a list $L$ contains values in the range $1,2,3,\ldots,b^{d}$ the runtime of radix sort is $O(d(n+b))$. Assume that $d=log_{b}(n)$, and that b is an constant, say 10, then $O(n * log_{b}(n))$. Unfortunately this is the same timecomplexity as in the other comparision-sort methods. However, if it's possible to set $b=n$ (more memory has to be allocated to the sub-routine counting sort), then $O(n)$.

In [372]:
N =list(np.arange(2,1000))
In [ ]:
 
In [375]:
TIME =list()
for _ in range(10):
    TIME.append(tzzzzimeIt(N))
In [368]:
VALS
Out[368]:
[]
In [355]:
len(A[0])
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-355-d7724f5e6bec> in <module>
----> 1 len(A[0])

TypeError: object of type 'float' has no len()
In [376]:
plt.plot(N, np.mean(TIME,0))
---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-376-25cbdede92b8> in <module>
----> 1 plt.plot(N, np.mean(TIME,0))

~/.local/lib/python3.6/site-packages/numpy/core/fromnumeric.py in mean(a, axis, dtype, out, keepdims)
   3116 
   3117     return _methods._mean(a, axis=axis, dtype=dtype,
-> 3118                           out=out, **kwargs)
   3119 
   3120 

~/.local/lib/python3.6/site-packages/numpy/core/_methods.py in _mean(a, axis, dtype, out, keepdims)
     57 
     58 def _mean(a, axis=None, dtype=None, out=None, keepdims=False):
---> 59     arr = asanyarray(a)
     60 
     61     is_float16_result = False

~/.local/lib/python3.6/site-packages/numpy/core/numeric.py in asanyarray(a, dtype, order)
    589 
    590     """
--> 591     return array(a, dtype, copy=False, order=order, subok=True)
    592 
    593 

KeyboardInterrupt: 
In [283]:
N
Out[283]:
[2,
 3,
 4,
 5,
 6,
 7,
 8,
 9,
 10,
 11,
 12,
 13,
 14,
 15,
 16,
 17,
 18,
 19,
 20,
 21,
 22,
 23,
 24,
 25,
 26,
 27,
 28,
 29,
 30,
 31,
 32,
 33,
 34,
 35,
 36,
 37,
 38,
 39,
 40,
 41,
 42,
 43,
 44,
 45,
 46,
 47,
 48,
 49,
 50,
 51,
 52,
 53,
 54,
 55,
 56,
 57,
 58,
 59]
In [291]:
TIME =list()
for _ in range(500):
    TIME.append(timeIt(N,2))
In [292]:
plt.plot(N, np.mean(TIME,0))
Out[292]:
[<matplotlib.lines.Line2D at 0x7efe02bb4320>]
In [334]:
TIME[0]
Out[334]:
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In [ ]: